THE DISTRIBUTION OF MOLECULES 99 



The difference between X4 and Xi or lo is so great that according to the 

 Boltzmann equation no appreciable number of molecules can remain iso- 

 lated in the surface. The few molecules that do exist as separate molecules, 

 however, must all lie flat in the surface because of the great difference 

 between Xo and Ai. 



If we consider lower members of the fatty acid series we find that the 

 difference between 1 for the single molecules and for those in clusters 

 becomes much smaller so that separate molecules do exist and therefore 

 the surface tension of water is decreased by even dilute films of these 

 acids in which a, the area per molecule, is very much greater than in ex- 

 panded films of palmitic acid. The values of 1 prove that in such two- 

 dimensional "gaseous" films the molecules lie flat in the surface. 



